Questions from Management Science

Q: The game of Chuck-a-Luck is played as follows

The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose $1. If your number appears x times, you win $x. On the av...

Q: You have $5 and your opponent has $10. You

You have $5 and your opponent has $10. You flip a fair coin and if heads comes up, your opponent pays you $1. If tails comes up, you pay your opponent $1. The game is finished when one player has all...

Q: Assume a very good NBA team has a 70% chance of

Assume a very good NBA team has a 70% chance of winning in each game it plays. During an 82 game season what is the average length of the team’s longest winning streak? What is the probability that th...

Q: For each part, make the change indicated, run the simulation

For each part, make the change indicated, run the simulation, and comment on any differences between your outputs and the outputs in the example. a. The cost of a new camera is increased to $500. b. T...

Q: You are going to play the Wheel of Misfortune Game against the

You are going to play the Wheel of Misfortune Game against the house. The wheel has 10 equally likely numbers: 5, 10, 15, 20, 25, 30, 35, 40, 45 ,and 50. The goal is to get a total as close as possibl...

Q: Consider the following card game. The player and dealer each receive

Consider the following card game. The player and dealer each receive a card from a 52-card deck. At the end of the game the player with the highest card wins; a tie goes to the dealer. (You can assume...

Q: Based on Morrison and Wheat (1984). When his team is

Based on Morrison and Wheat (1984). When his team is behind late in the game, a hockey coach usually waits until there is one minute left before pulling the goalie out of the game. Using simulation, i...

Q: You are playing Serena Williams in tennis, and you have a

You are playing Serena Williams in tennis, and you have a 42% chance of winning each point. (You are good!) a. Use simulation to estimate the probability you will win a particular game. Note that the...

Q: You now have $5000. You will toss a fair coin

You now have $5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you b...

Q: A farmer owns 450 acres of land. He is going to

A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $2000 profit, requires three workers, and requires two tons of fertilizer. Each...